The goal of this dissertation is to develop informative subject-specific simultaneous confidence bands (SCBs) for survival functions from right censored data. The approach is based on an extension of semiparametric random censorship models (SRCMs) to Cox regression, which produces reliable and more informative SCBs. SRCMs derive their rationale from their ability to utilize parametric ideas within the random censorship environment. Incorporating SRCMs into the existing framework produces more powerful procedures to analyze right censored data. The first part of the project focuses on proposing new estimators of Cox regression parameters and the cumulative baseline hazard function, and deriving their large sample properties. Under correct parametric specification, the proposed estimators of the regression parameter and the baseline cumulative hazard function are shown to be asymptotically as or more efficient than their standard Cox regression counterparts. Two real examples are provided. A further extension to the case of missing censoring indicators is also developed and an illustration with pseudo-real data is provided.
The second and final part of the project involves the deployment of the newly proposed estimators to obtain more informative SCBs for subject-specific survival curves. Simulation results are presented to compare the performance of the proposed SCBs with the SCBs that are based only on standard Cox. The new SCBs provide correct empirical coverage and are more informative. The proposed SCBs are illustrated with two real examples. An extension to handle missing censoring indicators is also outlined.
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